Examination of DFT and TDDFT methods I

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Density Functional Theory (DFT) and Time-Dependent DFT (TDDFT) are widely used for electronic structure calculations.
• Molecular Orbital (MO) theory and the Quantum Theory of Atoms in Molecules (QT-AIM) provide frameworks for understanding electronic properties.

Purpose of the Study:

• To investigate the behavior of DFT and TDDFT methods in describing the ground and excited states of ethene.
• To clarify the influence of electron correlation and MO occupation numbers on calculated properties.
• To explain the underestimation of excitation energies in TDDFT for specific excited states.

Main Methods:

• Application of DFT and TDDFT within MO theory.
• Utilizing the QT-AIM framework for analysis.
• Detailed investigation of the ground and pi --> pi* excited states of ethene.

Main Results:

• DFT methods incorporate electron correlation by modifying MO energies and electron density distributions.
• MO occupation numbers explain discrepancies in delocalization indices (DIs) between DFT and conventional correlated wave functions.
• TDDFT significantly underestimates excitation energies for ethene's pi --> pi* adiabatic excited states.

Conclusions:

• The underestimation of excitation energy by TDDFT in ethene is linked to the degeneracy of the Highest Occupied Molecular Orbital (HOMO) and the Lowest Unoccupied Molecular Orbital (LUMO).
• This degeneracy represents a specific case of charge transfer (CT) excited states, highlighting a limitation of TDDFT in such scenarios.
• Understanding these aspects is crucial for accurate electronic structure calculations and predicting excited-state properties.